School of Mathematical Sciences
Shanxi University
Taiyuan, Shanxi, 030006, China
email: hjhao@sxu.edu.cn
School of Mathematical Sciences
Shanxi University
Taiyuan, Shanxi, 030006, China
email: 1693229781@qq.com
Jianghao Hao, Dingkun Wang
Abstract:
In this article, we study the asymptotic stability of Bresse transmission systems
with two fractional dampings. The dissipation mechanism of control is given by the
fractional damping term and acts on two equations.
The relationship between the stability of the system, the fractional damping index
\(\theta\in[0,1]\) and the different wave velocities is obtained.
By using the semigroup method, we obtain the well-posedness of the system.
We also prove that when the wave velocities are unequal or equal with \(\theta\neq0\),
the system is not exponential stable, and it is polynomial stable.
In addition, the precise decay rate is obtained by the multiplier method and the
frequency domain method. When the wave velocities are equal with \(\theta=0\),
the system is exponential stable.
Submitted July 2, 2023. Published December 28, 2023.
Math Subject Classifications: 35B37, 35L55, 74D05, 93D15.
Key Words: Bresse system; fractional damping; asymptotic stability; exponential decay; polynomial decay.
DOI: 10.58997/ejde.2023.87
Show me the PDF file (465 KB), TEX file for this article.
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Jianghao Hao School of Mathematical Sciences Shanxi University Taiyuan, Shanxi, 030006, China email: hjhao@sxu.edu.cn |
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Dingkun Wang School of Mathematical Sciences Shanxi University Taiyuan, Shanxi, 030006, China email: 1693229781@qq.com |
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